Polynomial-time solution for the M-norm-constrained tensor estimator

Develop a polynomial-time method for computing or solving the M-norm-constrained tensor completion estimator under the model considered by Ghadermarzy et al.

Background

The paper reviews tensor-norm estimators as statistical benchmarks for low-rank tensor completion. In particular, it notes that Ghadermarzy et al. established favorable ambient-dimension dependence and nearly minimax-rate-optimal error bounds for M-norm- and max-qnorm-constrained estimators, although the rank dependence may not be optimal.

The unresolved computational issue is that the M-norm-constrained estimator has favorable statistical guarantees but lacks a known polynomial-time method. This problem is reported as an open computational limitation in the surrounding discussion of the statistical-to-computational gap in tensor completion.